An experiment is conducted where a self-driving car is set moving on a path along the circumference of a circular field of radius 5km. Two fixed points are chosen on the circle. A triangle is formed when these 3 points are connected [Assume the triangle formed to be completely random].Find the probability that the centre of the circle is present within the triangle.

The problem you're asking about is a well-known problem in geometry and probability. The surprising answer is that the probability that the center of the circle is inside the triangle is 1/4, or 25%.

Here's why:

1. Consider one of the fixed points and the center of the circle. This forms a line. The third point (the moving car) can be anywhere on the circumference of the circle.

2. If the car is on the half of the circle that makes an angle less than 180 degrees with the line from step 1, then the center of the circle will be inside the triangle. If the car is on the other half of the circle, the center will be outside the triangle.

3. Since the car is equally likely to be anywhere on the circle, the probability that it's on the "good" half of the circle is 1/2.

4. However, we have two fixed points, and we need to consider both of them. If we repeat the argument for the other fixed point, we find that it also has a 1/2 chance of making the center be inside the triangle.

5. But these two events are not independent: they can't both happen at the same time. If one fixed point makes the center be inside the triangle, the other fixed point makes the center be outside. So we can't just add the probabilities.

6. Instead, we need to find the probability that either one or the other happens, but not both. This is a classic problem in probability, and the answer is 1/4.

So the probability that the center of the circle is inside the triangle is 1/4.